Producing hydrocarbons from deep-sea reservoirs (1500-3000 m) raises a great variety of difficulties, mainly because of the high pressures and low temperatures prevailing at such depths. These difficulties are encountered in all the spheres of petroleum expertise: drilling and well servicing, process facilities (FPSO, FWHP, etc.) and their anchor systems, subsea technologies (multiphase pumping, subsea separation of petroleum fluid phases), risers and umbilicals or flow assurance.
As regards production proper, the operator is bound to give flow assurance despite many obstacles such as slugging, mineral or organic deposits, or hydrate formation. In the case of deep offshore drilling, hydrate formation is favoured by higher pressures and lower temperatures. Production stops during which the fluids cool down increase the hydrate formation risks still more.
Late detection of the presence of hydrates, notably through ignorance of the conditions of their formation in pipes, can lead to costly production problems: complete clogging of the production and/or transport pipes. It is therefore important for the operator to have means allowing to assess risks of any nature so as to implement control and servicing techniques and thus to be able to guarantee good flow of the circulating fluids.
In order to protect and thermally insulate subsea pipes, they are housed in an external tube withstanding the hydrostatic pressure. Most often, several pipes are grouped together so as to form bundles. These grouped pipes often have different functions. They are used for hydrocarbon production, injection of fluids into the reservoir, gas lift, circulation of heating fluid, etc. A low thermal conductivity lagging left at atmospheric pressure or under vacuum, with separations positioned at regular intervals for safety reasons, is for example interposed in the space between them.
With an efficient tool allowing continuous assessment of the risk of hydrate formation or of other deposits, the operator can take action by means of either pipe heating or additive injection. However, such a tool is difficult to set up and costly in calculating time, especially if the detailed composition of the petroleum fluids has to be taken into account. In order to study their behaviour more easily, it is well-known to describe them as a combination of a number of components or pseudo-components much smaller than the real number of constituents. This combination is referred to as a grouped composition as opposed to a detailed composition.
Patents FR-2,753,535 and FR-2,806,803 filed by the applicant describe methods for predicting the temperatures at which appear deposits such as waxes or paraffins in petroleum crudes whose constituents are grouped or lumped together into a smaller number of pseudo-components representing each several hydrocarbon classes and whose physico-chemical parameters are determined by combining the corresponding parameters of a certain number of pure hydrocarbons grouped together in a database. The pseudo-components of this grouped formulation are applied to a thermodynamic module allowing to determine various parameters indicative of the deposit formation conditions.
Various simulation softwares available on the market allow to model the behaviour of multiphase fluids circulating in pipelines.
The following patents or patent applications: U.S. Pat. No. 5,550,761, FR-2,756,044 (U.S. Pat. No. 6,028,992) and FR-2,756,045 (U.S. Pat. No. 5,960,187), FR-00/08,200 and FR-00/09,889 filed by the applicant, and the following publications:    Faille I. and Heintzé E., <<A rough finite volume scheme for modeling two-phase flow in a pipeline>>, Computers & Fluids 28 (1999), and    Pauchon C. et al., <<TACITE: a comprehensive mechanistic model for two-phase flow>>, 6th BHRG Multiphase International Conference, Cannes, France, June (1993)notably describe the TACITE (registered trade name) simulation code which simulates the transient behaviour of circulating multiphase fluids by continuously taking their composition into account. With such a predictive code, the production engineer can define the characteristics of fluid (notably hydrocarbon) transport systems: pipes, separators, valves, control systems, etc. One of the main goals of these simulation operations is to precisely predict the characteristics of transient flows in situations such as: inflow rate variation, pressure drop at the outlet, production stop and restart, pigging, appearance and propagation of slugs, formation of deposits likely to form under certain thermodynamic conditions, etc.
The flow modes of multiphase fluids in tubes are extremely varied and complex. Two-phase flows, for example, can be stratified, the liquid phase flowing in the lower part of the pipe, or intermittent with a succession of liquid and gas slugs, or disperse, the liquid being carried along in form of fine droplets. The flow mode and slippage between the phases vary notably with the inclination of the pipes to the horizontal and depend on the flow rate, the temperature, etc.
It can be reminded that the TACITE code allows to follow the composition variations of hydrocarbon mixtures. As already described in the aforementioned patents filed by the applicant, there is a mass conservation equation for each pseudo-component. There also is a momentum equation and an equation for the energy of the mixture. The corresponding equations are reminded hereafter, after a definition of the symbols and notations:                V absolute phase velocity        U surface velocity        R volume fraction per phase        ρ phase density        H phase enthalpy        E internal energy        P pressure of the mixture        Tw wall friction        Qw wall heat flow between the pipeline and the surrounding medium        θ pipeline inclination        g gravity        S pipeline section        x mass fraction of the component in a given phase        p number of phases (1 to 3)        N number of components        k phase index        i component index        m mixture index        The mass equilibrium equation for each component is:                                                         ∂                              ∂                t                                      ⁢                          {                                                ∑                                      k                    =                    1                                    p                                ⁢                                                                   ⁢                                  S                  ⁡                                      (                                                                  ρ                        k                                            ⁢                                              R                        k                                            ⁢                                              x                        i                        k                                                              )                                                              }                                +                                    ∂                              ∂                x                                      ⁢                          {                                                ∑                                      k                    =                    1                                    p                                ⁢                                                                   ⁢                                  S                  ⁡                                      (                                                                  ρ                        k                                            ⁢                                              R                        k                                            ⁢                                              x                        i                        k                                            ⁢                                              V                        k                                                              )                                                              }                                      =                  0          ⁢                                           ⁢                                    (                                                i                  =                  1                                ,                ⋯                ⁢                                                                   ,                N                            )                        .                                              (        1        )                    The momentum equilibrium equation of the mixture is:                                                         ∂                              ∂                t                                      ⁢                          {                                                ∑                                      k                    =                    1                                    p                                ⁢                                                                   ⁢                                  S                  ⁡                                      (                                                                  ρ                        k                                            ⁢                                              R                        k                                            ⁢                                              V                        k                                                              )                                                              }                                +                                    ∂                              ∂                x                                      ⁢                          {                                                (                                                            ∑                                              k                        =                        1                                            p                                        ⁢                                                                                                               ⁢                                              S                        ⁡                                                  (                                                                                    ρ                              k                                                        ⁢                                                          R                              k                                                        ⁢                                                          V                              k                              2                                                                                )                                                                                                      )                                +                P                            }                                      =                              S            ⁡                          (                                                T                  w                                -                                                      ρ                    m                                    ⁢                  g                  ⁢                                                                           ⁢                  sin                  ⁢                                                                           ⁢                  θ                                            )                                .                                    (        2        )                    The mixture energy equilibrium equation is:                                                         ∂                              ∂                t                                      ⁢                          {                                                ∑                                      k                    =                    1                                    p                                ⁢                                                                   ⁢                                  S                  ⁡                                      (                                                                  ρ                        k                                            ⁢                                              E                        k                                                              )                                                              }                                +                                    ∂                              ∂                x                                      ⁢                          {                                                ∑                                      k                    =                    1                                    p                                ⁢                                                                   ⁢                                  S                  ⁡                                      (                                                                  ρ                        k                                            ⁢                                              R                        k                                            ⁢                                              V                        k                                            ⁢                                              H                        k                                                              )                                                              }                                      =                              S            ⁡                          (                                                Q                  w                                -                                                      ρ                    m                                    ⁢                                      gU                    m                                    ⁢                                                                           ⁢                  sin                  ⁢                                                                           ⁢                  θ                                            )                                .                                    (        3        )                    
Numerical Scheme
The numerical scheme is conservative and non-dissipative. It provides a good mass and energy balance at any point of the pipe and at any time. A mixed implicit/explicit scheme is used to optimize the computing time and the capacity of following the void fraction wave fronts, which is particularly important when the configuration of the terrain followed by the pipeline or its own configuration favours the formation of liquid slugs with propagation of void waves in the two opposite directions of the pipeline, phenomena commonly referred to by specialists as terrain slugging or severe slugging.
Thermodynamic Module
The TACITE simulation code comprises an integrated thermodynamic flash module, i.e. an integrated subprogram intended to compute the thermodynamic properties (liquid-vapour equilibrium, composition of each phase) by means of an equation of state. This flash carries out two-phase and three-phase thermodynamic equilibrium computations for hydrocarbon mixtures including water. The Peng-Robinson (1) and Soave-Redlich-Kwong (2) cubic equations of state are used for modelling the thermodynamic properties at phase equilibrium. These equations are defined in the following publications:    Peng D. Y. et al., <<A new two-constant equation of state>>, Ind. Eng. Chem Fund. 15, 59 (1976),    Soave G., <<Equilibrium constants from a modified Redlich-Kwong equation of state>>, Chem. Eng. Sci. 27, 1197 (1972).
In both cases, the molecular volumes can be corrected by the Peneloux method described in the following publication:    Péneloux A. et al., <<A consistent correction for Redlich-Kwong-Soave volumes>>, Fluid Phase Equilibria 8, 7 (1982).
The module referred to as flash allows precise monitoring of the composition of the fluids, in space as well as in time, throughout the simulation.
This composition monitoring makes the TACITE code particularly well-suited for precise prediction of the hydrate formation risk, as described below.
Hydrodynamic Module
The hydrodynamic module computes the flow regime, the phase slip velocity and the friction terms.